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<b>thus </b><a NAME="E1:30_1_1"/>
 ex <font color="Olive" title="b1">Un</font> being  <a href="nagata_1.html#NM1" title="NAGATA_1:NM.1">FamilySequence</a> of <font color="Maroon" title="c1">T</font> st <font color="Olive" title="b1">Un</font> is <a href="nagata_1.html#V3" title="NAGATA_1:attr.3">sigma_locally_finite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c2">Un</font> being   <a href="nagata_1.html#NM1" title="NAGATA_1:NM.1">FamilySequence</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E2:30_1_1_1"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">Un</font> is <a href="nagata_1.html#V2" title="NAGATA_1:attr.2">sigma_discrete</a>
 <b>by </b><i><a class="txt" href="nagata_1.html#E18"><i><font color="Green" title="E12">Lm5</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">Un</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><a NAME="E1:30_1_1_1_1"/>
<font color="Maroon" title="c2">Un</font> <a href="nagata_1.html#K1" title="NAGATA_1:func.1">.</a> <font color="Maroon" title="c3">n</font> is <a href="nagata_1.html#V1" title="NAGATA_1:attr.1">discrete</a>
 <b>by </b><i><a class="txt" href="nagata_1.html#E2:30_1_1_1"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="nagata_1.html#D2" target="_self" title="NAGATA_1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E2:30_1_1_1_1"/>
<font color="Maroon" title="c2">Un</font> <a href="nagata_1.html#K1" title="NAGATA_1:func.1">.</a> <font color="Maroon" title="c3">n</font> is <a href="pcomps_1.html#V1" title="PCOMPS_1:attr.1">locally_finite</a>
 <b>by </b><i><a class="ref" href="nagata_1.html#T11" target="_self" title="NAGATA_1:th.11">Th11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:30_1_1_1"/>
<font color="Maroon" title="c2">Un</font> is <a href="nagata_1.html#V3" title="NAGATA_1:attr.3">sigma_locally_finite</a>
 <b>by </b><i><a class="ref" href="nagata_1.html#D3" target="_self" title="NAGATA_1:def.3">Def3</a></i>;<br/>


</div><b>end;</b></div>


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